Lecture Strength of Materials I - Chapter 6: Torsion. The following will be discussed in this chapter: Introduction, torsional loads on circular shafts, strength condition and stiffness condition, statically indeterminate problem, strain energy, examples. | STRENGTH OF MATERIALS 1 10 2013 TRAN MINH TU - University of Civil Engineering 1 Giai Phong Str. 55 Hai Ba Trung Dist. Hanoi Vietnam CHAPTER 6 TORSION 1 10 2013 Contents . Introduction . Torsional Loads on Circular Shafts . Strength Condition and stiffness condition . Statically Indeterminate Problem . Strain Energy . Examples Home s works 1 10 2013 3 . Introduction 1 10 2013 4 . Introduction 1 10 2013 5 . Introduction Torsion members the slender members subjected to torsional loading that is loaded by couple that produce twisting of the member about its axis Examples A torsional moment torque is applied to the lug-wrench shaft the shaft transmits the torque to the generator the drive shaft of an automobile. Torsional Loads on Circular Shafts the torsional moment or couple A F x Q2 B C Q1 t z 2 T t T 1 1 2 y 1 10 2013 6 . Introduction Internal torsional moment diagram Using method of section Sign convention of Mz - Positive clockwise - Negative counterclockwise Mz gt 0 M z 0 Mz y y z z x x 1 10 2013 7 . Torsion of Circular Shafts . Simplifying assumptions 1 10 2013 8 . Torsion of Circular Shafts gt In the cross-section only shear stress exists . Compatibility Consider the portion of the shaft shown in the figure CD before deformation CD after deformation - From the geometry DD d dz d gt The Shear strain dz - d the angle of twist - Following Hooke s law d G G 1 10 2013 dz 9 . Torsion of Circular Shafts . Equilibrium d 2 d M z dA G dA G Ip A dz A dz d M z the rate of twist dz GI p . Torsion formulas Shearing stress Mz internal torsional moment Mz Ip polar moment of inertia Ip radial position 1 10 2013 10 . Torsion of Circular Shafts - Maximum shearing stress Mz Mz max R Ip Wp - Wp - Section modulus of torsion Angle of twist c a b O A B L A L M z dz M dz rad From AB z 1 10 2013 B GI p 0 GI p 11 . Torsion of Circular Shafts M zL Mz const AB GI p GI p Multiply torques GIp stiffness of torsional .
